Rotating machines are important parts that are incorporated and used in various apparatuses, and improvements are repeatedly made for high performance. In order to support the designing of a new rotating machine, numerical analysis of the performance by a finite element method is generally performed by changing the shape of the rotating machine.
The finite element method is a method for performing numerical calculation by representing an object to be analyzed by a combination of a plurality of polyhedral elements, and is widely used for the analysis of the structure of three-dimensional objects. In the case where the finite element method is used for the numerical analysis of a rotating machine, in order to analyze the magnetic field between a stator and a rotor, it is necessary to generate a three-dimensional mesh representing the spatial area between the stator and the rotor as well as the stator and the rotor by a combination of a plurality of polyhedral elements. Moreover, in order to analyze the magnetic field while rotating the rotor, it is necessary to take into account the rotational motion in generating the three-dimensional mesh.
Conventionally, a three-dimensional mesh of the rotating machine is generated as follows. A boundary surface in the form of a cylindrical surface is set in the spatial area of the rotating machine, and a space on the stator side and a space on the rotor side including the spatial area with the boundary surface therebetween are represented by combinations of a plurality of polyhedrons, respectively, on a two-dimensional plane perpendicular to the rotation axis to generate two-dimensional meshes. At this time, portions of the two-dimensional meshes on the stator side and the rotor side, which come into contact with the boundary surface, are equally divided in the rotation direction and arranged to match each other at the boundary surface. Next, the generated two-dimensional meshes are stacked in the direction of the rotation axis to generate a three-dimensional mesh representing the rotating machine including the spatial area. By shifting the three-dimensional mesh on the rotor side from the boundary surface by one element with respect to the stator side, the rotor can be rotated, and the magnetic field of the rotating machine can be analyzed while rotating the rotor.
Further, Japanese Patent Application Laid-Open No. 2001-155055 discloses a method for generating a three-dimensional mesh of a rotating machine by generating three-dimensional meshes on the stator side and the rotor side independently of each other, providing a gap between them, and generating a three-dimensional mesh of the gap by filling the gap with polyhedrons by an automatic element division method. In the case where a three-dimensional mesh generated by this method is used, analysis of the magnetic field of the rotating machine while rotating the rotor can be performed by regenerating a three-dimensional mesh of the gap whenever the rotor is rotated.
One of the problems of the rotating machine is the torque variation, which occurs because the magnitude of magnetic flux that generates the rotating force in the rotor changes depending on the positional relationship between the stator and the rotor, and this torque variation will cause vibration and noise of the rotating machine. In order to reduce the torque variation, used is a rotating machine having skew that is a structure of the stator or the rotor twisted in the direction of the rotation axis. However, in order to perform numerical analysis of the rotating machine having skew by the finite element method, there is the problem that it is impossible to use a conventional three-dimensional mesh generating method in which two-dimensional meshes generated on a plane perpendicular to the rotation axis are stacked in the direction of the rotation axis, because the shape of the rotating machine is not symmetric about the plane perpendicular to the rotation axis.
In addition, according to the method disclosed in Japanese Patent Application Laid-Open No. 2001-155055, since the three-dimensional meshes on the stator side and the rotor side are generated independently of each other, it is possible to generate a three-dimensional mesh of a rotating machine having skew, but this method has the problem that it takes a long time for calculation in the analysis because a three-dimensional mesh needs to be regenerated whenever rotation is performed, and the problem that a process for giving the three-dimensional mesh periodicity in the rotation direction is additionally required because the three-dimensional mesh regenerated whenever rotation is performed is irregular.